Mr. Evans, unopposed on his party's ballot in the May 25 state primary, is a middle-road Democrat who for the last several months has been doggedly battling against his state's serious economic problems.

Larry LaRocca, a one-time aide to former Sen. Frank Church (D) of Idaho, was unopposed for the Democratic nomination to challenge First District Rep. Larry E. Craig (R) in November.

Neither Mr. Craig nor Second District Rep. George Hansen (R) was opposed on the GOP ballot.

Mr. LaRocca will be the underdog in the contest with Craig, but some observers see a slight chance for an upset. Richard Stallings, Ricks College history professor who won the Democratic nomination in the Second District, is seen providing only token opposition for Mr. Hansen on Nov. 2.

There is no US Senate race in Idaho this year. The terms of Republican Sens. James A. McClure and Steven D. Symms expire in 1985 and 1987, respectively.

John Evans, who became governor in 1977 when President Carter named Cecil D. Andrus as his secretary of the interior, was elected to a full term in 1978. In recent months he has been struggling with high unemployment in Idaho's two chief industries -- forest products and mining. At the same time, the declining economy has shrunk revenues. The state budget is expected to be $12 million in the red at the end of the fiscal year. To meet a state constitutional ban on unbalanced budgets, the governor has cut the workweek for state employees to 32 hours. Observers say additional measures may be necessary, possibly a special legislative session.

How much this will be blamed on Democrat Evans and how much on the economic policies of President Reagan could determine the outcome of the gubernatorial race. However, Evans is a popular governor and there is a general feeling in the state that he has done everything possible to counter the recession.

In the next two weeks three more Western states will have primaries -- New Mexico June 1, California and Montana June 8. Eight more Western states will hold primaries in September for the Nov. 2 general election. Oregon started things off May 18 when Republicans renominated Gov. Victor L. Atiyeh and Democrats selected state Sen. Ted Kulongoski to challenge Mr. Atiyeh in November.

Here is a brief look at the three upcoming primaries:

* New Mexico. With Republican US Sen. Harrison Schmitt labeled ''vulnerable'' in his bid for a second term in November, it appears Democratic voters in New Mexico will choose state Attorney General Jeff Bingaman to challenge the former astronaut.

Mr. Bingaman was favored by 52 percent of voters sampled in a recent poll, increasing his previous lead over former Gov. Jerry Apodaca, who had a 29 percent rating.

Only 12 Republican-held seats in the US Senate are at stake this year, but considering the thin GOP majority in that chamber, the national party is expected to make a special effort to hold every one of them, including Senator Schmitt's.

Polls indicate that New Mexico Democrats will choose former state Attorney General Tony Anaya over veteran state Sen. Aubrey Dunn as their nominee to succeed Democratic Gov. Bruce King, who by law cannot succeed himself. The Republican nomination is more in doubt.

In the Republican gubernatorial contest, a recent voter sampling showed former state Sen. Bill Segal leading another former state senator, John B. Irick , by 40 to 25 percent. But there was a whopping 30 percent undecided.

Four Democrats are fighting for the nomination to the US House of Representatives in the new Third Distict. New Mexico, with two well-entrenched Republican congressmen, picked up its third House seat in the 1980 census. The new district, in the northern part of the state, is preponderantly Hispanic and Democratic.

The Republican senatorial nomination at present seems a tossup between US Rep. Barry M. Goldwater Jr. and San Diego Mayor Pete Wilson. US Rep. Paul N. (Pete) McCloskey is not expected to finish higher than third.

In a close contest for the GOP gubernatorial nomination, Lt. Gov. Mike Curb is thought to have a slight edge over state Attorney General George Deukmejian. Mr. Deukmejian favors the massive peripheral canal water project and Mr. Curb is against it. The canal vote (Proposition 9 on the referendum ballot) will be close, too.

* Montana. This will be a quiet primary in terms of national-level offices. Democratic Gov. Ted Schwinden's term lasts through 1984; the state's two congressmen, Republican Ron Marlenee and Democrat Pat Williams, are unopposed in the primaries and are expected to win reelection Nov. 2.

Although a spirited fall campaign for the US Senate is expected, the two major candidates are known in advance of the primary. Democratic US Sen. John Melcher faces considerable difficulty in his bid for a second term. Even before financial expert Larry Williams became the unopposed Republican candidate the senator was under attack from a conservative political action committee.

The national Republican party will become involved, since the Montana situation presents an opportunity to increase -- or at least maintain -- its Senate majority.